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Journal of Scientific Computing

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05-09-2018

Hybridized Discontinuous Galerkin Methods for Wave Propagation

Authors: P. Fernandez, A. Christophe, S. Terrana, N. C. Nguyen, J. Peraire

Published in: Journal of Scientific Computing | Issue 3/2018

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Abstract

We present the recent development of hybridizable and embedded discontinuous Galerkin (DG) methods for wave propagation problems in fluids, solids, and electromagnetism. In each of these areas, we describe the methods, discuss their main features, display numerical results to illustrate their performance, and conclude with bibliography notes. The main ingredients in devising these DG methods are (1) a local Galerkin projection of the underlying partial differential equations at the element level onto spaces of polynomials of degree k to parametrize the numerical solution in terms of the numerical trace; (2) a judicious choice of the numerical flux to provide stability and consistency; and (3) a global jump condition that enforces the continuity of the numerical flux to obtain a global system in terms of the numerical trace. These DG methods are termed hybridized DG methods, because they are amenable to hybridization (static condensation) and hence to more efficient implementations. They share many common advantages of DG methods and possess some unique features that make them well-suited to wave propagation problems.

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Note the amplification factor \(N_1\) in the y-axis is a logarithmic quantity.

Note the amplitude of the instabilities in Fig. 3 is non-dimensionalized with respect to the freestream velocity.

The mismatch between the simulation and the experimental data near the leading edge is due to the missing vortex upwash induced by the finite extent of the computational domain, and not due to discretization errors [49, 50].

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Title: Hybridized Discontinuous Galerkin Methods for Wave Propagation
Authors: P. Fernandez
A. Christophe
S. Terrana
N. C. Nguyen
J. Peraire
Publication date: 05-09-2018
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 3/2018
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-018-0811-x

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